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The nearest-neighbour technique is used to infer competition and facilitation between the three most abundant species in a semi-arid region of western South Africa. Relationships among the shrubs Leipoldtia schultzei and Ruschia robusta. which are leaf-succulent members of the Mesembryanthemaceae (’mesembs’) and Hirpicium alienatum a non-succulent Asteraceae, were compared on two adjacent sites with different histories of browsing intensity. Competition was more prevalent and more important than facilitation. The only evidence for facilitation was found at the heavily-browsed site where the palatable Hirpicium was larger under the unpalatable Leipoldtia. Generally the prevalence and importance of competition was reduced at the heavily-browsed site. Strong evidence was obtained for intraspecific competition in each of the three species: also, competition was evident between the two mesembs, where Leipoldtia was competitively dominant over Ruschia, although neither species inhibited Hirpicium. Minimal competition between the mesembs and the asteraceous shrub was interpreted in terms of differentiation in rooting depth. and competition within the mesembs, in terms of overlap in rooting depth. The mesembs had the bulk of their roots in the top 5 cm of soil. while the asteraceous shrub had the bulk of its roots, and all its fine roots, at greater depths. The shallow-rooted morphology of the mesembs is well adapted to utilize small rainfall events, which occur frequently in the Succulent Karoo, and do not penetrate the soil deeply. Modifications of existing methods are applied for analysing nearest-neighbour interactions.